Approximability of the independent feedback vertex set problem for bipartite graphs

Yuma Tamura, Takehiro Ito, Xiao Zhou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Given a graph G with n vertices, the independent feedback vertex set problem is to find a vertex subset F of G with the minimum number of vertices such that F is both an independent set and a feedback vertex set of G, if it exists. This problem is known to be NP-hard for bipartite planar graphs. In this paper, we study the approximability of the problem. We first show that, for any fixed ε > 0, unless P = NP, there exists no polynomial-time n1−ε-approximation algorithm even for bipartite planar graphs. This gives a contrast to the existence of a polynomial-time 2-approximation algorithm for the original feedback vertex set problem on general graphs. We then give an α(Δ − 1)/2-approximation algorithm for bipartite graphs G of maximum degree Δ, which runs in O(t(G)+Δn) time, under the assumption that there is an α-approximation algorithm for the original feedback vertex set problem on bipartite graphs which runs in O(t(G)) time.

Original languageEnglish
Title of host publicationWALCOM
Subtitle of host publicationAlgorithms and Computation - 14th International Conference, WALCOM 2020, Proceedings
EditorsM. Sohel Rahman, Kunihiko Sadakane, Wing-Kin Sung
PublisherSpringer
Pages286-295
Number of pages10
ISBN (Print)9783030398804
DOIs
Publication statusPublished - 2020 Jan 1
Event14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020 - Singapore, Singapore
Duration: 2020 Mar 312020 Apr 2

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12049 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference14th International Conference and Workshops on Algorithms and Computation, WALCOM 2020
CountrySingapore
CitySingapore
Period20/3/3120/4/2

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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